GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
The shaded region in the figure above represents a rectangular frame
[#permalink]
20 Sep 2021, 04:53
20 Sep 2021, 04:53
Expert Reply
1
Bookmarks
00:00
Question Stats:
50% (03:28) correct
50% (02:17) wrong based on 4 sessions
Hide Show timer Statistics
The shaded region in the figure above represents a rectangular frame with length 18 inches and width 15 inches. The frame encloses a rectangular picture that has the same area as the frame itself. If the length and width of the picture have the same ratio as the lenght and width of the frame, what is the length of the picture, in inches?
A. \(9\sqrt2\)
B. \(\frac {3}{2}\)
C. \(\frac {9}{\sqrt2}\)
D. \(15 ( 1 - \frac {1}{\sqrt2})\)
E. \(\frac {9}{2}\)
Re: The shaded region in the figure above represents a rectangular frame
[#permalink]
20 Sep 2021, 07:40
20 Sep 2021, 07:40
1
Let the internal rectangle be of Length L and Width(W).
So given Area of shaded is = area of internal rectangle , \(18 * 15 = 2 * L * W\).
Draw a diagonal and there will be 2 similar triangles, so \(\frac{18}{15} = \frac{L}{W}\).
Solve for L and it will be \(9\sqrt{2}\)
So given Area of shaded is = area of internal rectangle , \(18 * 15 = 2 * L * W\).
Draw a diagonal and there will be 2 similar triangles, so \(\frac{18}{15} = \frac{L}{W}\).
Solve for L and it will be \(9\sqrt{2}\)
Re: The shaded region in the figure above represents a rectangular frame
[#permalink]
22 Nov 2021, 02:49
22 Nov 2021, 02:49
1
Let \(l\) and \(w\) be the length and width of picture respectively that is being enclosed within the picture
Length and width of frame is given as \(18\) and \(15\) respectively.
length and width of the picture have the same ratio as the length and width of the frame, which means \(\frac{l}{w} = \frac{18}{15} = \frac{6}{5} \Rightarrow w = \frac{5}{6}l\)
Area of the frame itself = Total area of entire square - Area of the picture = \(18*15 - l*b\)
The frame encloses a rectangular picture that has the same area as the frame itself, meaning
\(18*15 - lb = lb\)
\(18*15 = 2lb = 2(l)(\frac{5}{6}l) = \frac{5}{3}l^2\)
\(l^2 = \frac{18*15*3}{5} = 18*3*3 = 9*2*9 = 9^2*2\)
\(l = \sqrt{9^2*2} = 9\sqrt{2}\)
Hence, Answer is A
Length and width of frame is given as \(18\) and \(15\) respectively.
length and width of the picture have the same ratio as the length and width of the frame, which means \(\frac{l}{w} = \frac{18}{15} = \frac{6}{5} \Rightarrow w = \frac{5}{6}l\)
Area of the frame itself = Total area of entire square - Area of the picture = \(18*15 - l*b\)
The frame encloses a rectangular picture that has the same area as the frame itself, meaning
\(18*15 - lb = lb\)
\(18*15 = 2lb = 2(l)(\frac{5}{6}l) = \frac{5}{3}l^2\)
\(l^2 = \frac{18*15*3}{5} = 18*3*3 = 9*2*9 = 9^2*2\)
\(l = \sqrt{9^2*2} = 9\sqrt{2}\)
Hence, Answer is A
